{"id":"https://openalex.org/W2236716729","doi":"https://doi.org/10.1007/s40314-015-0293-5","title":"Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach","display_name":"Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach","publication_year":2015,"publication_date":"2015-10-31","ids":{"openalex":"https://openalex.org/W2236716729","doi":"https://doi.org/10.1007/s40314-015-0293-5","mag":"2236716729"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-015-0293-5","doi":"https://doi.org/10.1007/s40314-015-0293-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-015-0293-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071037587","display_name":"Masoud Sanei","orcid":"https://orcid.org/0000-0002-2097-9354","observed_orcids":["https://orcid.org/0000-0002-2097-9354"]},"institutions":[{"id":"https://openalex.org/I110525433","display_name":"Islamic Azad University, Tehran","ror":"https://ror.org/01kzn7k21","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433"]},{"id":"https://openalex.org/I41775361","display_name":"Islamic Azad University Central Tehran Branch","ror":"https://ror.org/03a11m818","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I41775361"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Masoud Sanei","raw_affiliation_strings":["Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran","institution_ids":["https://openalex.org/I110525433","https://openalex.org/I41775361"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001831075","display_name":"Ali Mahmoodirad","orcid":"https://orcid.org/0000-0002-0018-5389","observed_orcids":["https://orcid.org/0000-0002-0018-5389"]},"institutions":[{"id":"https://openalex.org/I4210158817","display_name":"Islamic Azad University, Masjed Soleyman","ror":"https://ror.org/05m905s87","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210158817"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Mahmoodirad","raw_affiliation_strings":["Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran","institution_ids":["https://openalex.org/I4210158817"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068245012","display_name":"Sadegh Niroomand","orcid":"https://orcid.org/0000-0001-8196-3906","observed_orcids":["https://orcid.org/0000-0001-8196-3906"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sadegh Niroomand","raw_affiliation_strings":["Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran"],"raw_orcid":"https://orcid.org/0000-0001-8196-3906","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024085924","display_name":"Ali Jamalian","orcid":"https://orcid.org/0000-0001-6237-3118","observed_orcids":["https://orcid.org/0000-0001-6237-3118"]},"institutions":[{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Jamalian","raw_affiliation_strings":["Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran","institution_ids":["https://openalex.org/I877176835"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013557629","display_name":"Shahin Gelareh","orcid":"https://orcid.org/0000-0002-6606-9698","observed_orcids":["https://orcid.org/0000-0002-6606-9698"]},"institutions":[{"id":"https://openalex.org/I44563897","display_name":"Universit\u00e9 d'Artois","ror":"https://ror.org/053x9s498","country_code":"FR","type":"education","lineage":["https://openalex.org/I44563897"]},{"id":"https://openalex.org/I59807433","display_name":"Universit\u00e9 Lille Nord de France","ror":"https://ror.org/03btvgn05","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970","https://openalex.org/I59807433"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Shahin Gelareh","raw_affiliation_strings":["Laboratoire G\u00e9nie Informatique et Automatique, Universit\u00e9 d\u2019Artois, 62400, B\u00e9thune, France","Universit\u00e9 Lille Nord de France, 59000, Lille, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire G\u00e9nie Informatique et Automatique, Universit\u00e9 d\u2019Artois, 62400, B\u00e9thune, France","institution_ids":["https://openalex.org/I44563897"]},{"raw_affiliation_string":"Universit\u00e9 Lille Nord de France, 59000, Lille, France","institution_ids":["https://openalex.org/I59807433"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5068245012"],"corresponding_institution_ids":[],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":2.6665,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.88867758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"36","issue":"3","first_page":"1217","last_page":"1237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.03449999913573265,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.8149999976158142},{"id":"https://openalex.org/keywords/dual-decomposition","display_name":"dual decomposition","score":0.9879999756813049},{"id":"https://openalex.org/keywords/lagrangian-heuristic","display_name":"Lagrangian heuristic","score":0.7950000166893005},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.7689999938011169},{"id":"https://openalex.org/keywords/large-scale-optimization","display_name":"large-scale optimization","score":0.6980000138282776},{"id":"https://openalex.org/keywords/transportation-engineering","display_name":"transportation engineering","score":0.4740000069141388}],"concepts":[{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.935523509979248},{"id":"https://openalex.org/C2984553159","wikidata":"https://www.wikidata.org/wiki/Q13579421","display_name":"Fixed charge","level":2,"score":0.7444956302642822},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7079436779022217},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.689728856086731},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.6042495369911194},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5944254994392395},{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.5917165279388428},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.500786542892456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4998588562011719},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4908169209957123},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.42434677481651306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31199097633361816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20358595252037048},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0930122435092926},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C41999313","wikidata":"https://www.wikidata.org/wiki/Q489328","display_name":"Molecular physics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s40314-015-0293-5","doi":"https://doi.org/10.1007/s40314-015-0293-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-015-0293-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04538535v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-04538535","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational & Applied Mathematics, 2015, 36 (3), pp.1217-1237. ⟨10.1007/s40314-015-0293-5⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8970999717712402,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1965593276","https://openalex.org/W1966458658","https://openalex.org/W1968297841","https://openalex.org/W1972905263","https://openalex.org/W1977603313","https://openalex.org/W1978480513","https://openalex.org/W1981364505","https://openalex.org/W1982945930","https://openalex.org/W1985029326","https://openalex.org/W1996180761","https://openalex.org/W2001614877","https://openalex.org/W2001912652","https://openalex.org/W2004436663","https://openalex.org/W2005426578","https://openalex.org/W2006592884","https://openalex.org/W2008428752","https://openalex.org/W2011080858","https://openalex.org/W2012738290","https://openalex.org/W2019842383","https://openalex.org/W2022606608","https://openalex.org/W2024060531","https://openalex.org/W2027358744","https://openalex.org/W2034203304","https://openalex.org/W2038770643","https://openalex.org/W2041088973","https://openalex.org/W2045029812","https://openalex.org/W2047128008","https://openalex.org/W2047577782","https://openalex.org/W2055827613","https://openalex.org/W2058198940","https://openalex.org/W2059243123","https://openalex.org/W2061713434","https://openalex.org/W2061917827","https://openalex.org/W2066370001","https://openalex.org/W2079195297","https://openalex.org/W2090286482","https://openalex.org/W2094252279","https://openalex.org/W2107919572","https://openalex.org/W2116028184","https://openalex.org/W2127061258","https://openalex.org/W2127872150","https://openalex.org/W2131512748","https://openalex.org/W2150368518","https://openalex.org/W2166855192","https://openalex.org/W2169337137","https://openalex.org/W2170947141","https://openalex.org/W4230379687","https://openalex.org/W4236384091","https://openalex.org/W4256046638"],"related_works":["https://openalex.org/W2740877406","https://openalex.org/W1972905263","https://openalex.org/W2001571342","https://openalex.org/W2069737189","https://openalex.org/W2001614877","https://openalex.org/W2017969921","https://openalex.org/W3007481928","https://openalex.org/W2585675459","https://openalex.org/W6983227735","https://openalex.org/W6983417744"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}